%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG176+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:07:06 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG176+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 19:38:30 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.26 Command-line arguments: --no-flatten-goal
% 0.20/0.26
% 0.20/0.26 % SZS status Theorem
% 0.20/0.26
% 0.20/0.27 % SZS output start Proof
% 0.20/0.27 Axiom 1 (ax3): sorti1(u) = true.
% 0.20/0.27 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.27 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.20/0.27 Axiom 4 (ax4_1): ifeq(sorti2(X), true, sorti2(v(X)), true) = true.
% 0.20/0.27 Axiom 5 (co1_3): ifeq(sorti2(X), true, sorti1(j(X)), true) = true.
% 0.20/0.27 Axiom 6 (co1): ifeq(sorti1(X), true, sorti2(h(X)), true) = true.
% 0.20/0.27 Axiom 7 (co1_2): ifeq2(sorti1(X), true, j(h(X)), X) = X.
% 0.20/0.27 Axiom 8 (ax4): ifeq2(sorti2(X), true, op2(v(X), X), v(X)) = v(X).
% 0.20/0.27 Axiom 9 (co1_4): ifeq2(sorti2(X), true, ifeq2(sorti2(Y), true, op1(j(Y), j(X)), j(op2(Y, X))), j(op2(Y, X))) = j(op2(Y, X)).
% 0.20/0.27
% 0.20/0.27 Lemma 10: op2(v(h(u)), h(u)) = v(h(u)).
% 0.20/0.27 Proof:
% 0.20/0.27 op2(v(h(u)), h(u))
% 0.20/0.27 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.27 ifeq2(true, true, op2(v(h(u)), h(u)), v(h(u)))
% 0.20/0.27 = { by axiom 6 (co1) R->L }
% 0.20/0.27 ifeq2(ifeq(sorti1(u), true, sorti2(h(u)), true), true, op2(v(h(u)), h(u)), v(h(u)))
% 0.20/0.27 = { by axiom 1 (ax3) }
% 0.20/0.27 ifeq2(ifeq(true, true, sorti2(h(u)), true), true, op2(v(h(u)), h(u)), v(h(u)))
% 0.20/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.27 ifeq2(sorti2(h(u)), true, op2(v(h(u)), h(u)), v(h(u)))
% 0.20/0.27 = { by axiom 8 (ax4) }
% 0.20/0.27 v(h(u))
% 0.20/0.27
% 0.20/0.27 Goal 1 (ax3_1): tuple(op1(X, u), sorti1(X)) = tuple(X, true).
% 0.20/0.27 The goal is true when:
% 0.20/0.27 X = j(v(h(u)))
% 0.20/0.27
% 0.20/0.27 Proof:
% 0.20/0.27 tuple(op1(j(v(h(u))), u), sorti1(j(v(h(u)))))
% 0.20/0.27 = { by axiom 7 (co1_2) R->L }
% 0.20/0.27 tuple(op1(j(v(h(u))), ifeq2(sorti1(u), true, j(h(u)), u)), sorti1(j(v(h(u)))))
% 0.20/0.27 = { by axiom 1 (ax3) }
% 0.20/0.27 tuple(op1(j(v(h(u))), ifeq2(true, true, j(h(u)), u)), sorti1(j(v(h(u)))))
% 0.20/0.27 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.27 tuple(op1(j(v(h(u))), j(h(u))), sorti1(j(v(h(u)))))
% 0.20/0.27 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.28 tuple(ifeq2(true, true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 4 (ax4_1) R->L }
% 0.20/0.28 tuple(ifeq2(ifeq(sorti2(h(u)), true, sorti2(v(h(u))), true), true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.28 tuple(ifeq2(ifeq(ifeq(true, true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 1 (ax3) R->L }
% 0.20/0.28 tuple(ifeq2(ifeq(ifeq(sorti1(u), true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 6 (co1) }
% 0.20/0.28 tuple(ifeq2(ifeq(true, true, sorti2(v(h(u))), true), true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.28 tuple(ifeq2(sorti2(v(h(u))), true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.28 tuple(ifeq2(true, true, ifeq2(sorti2(v(h(u))), true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), j(op2(v(h(u)), h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 6 (co1) R->L }
% 0.20/0.28 tuple(ifeq2(ifeq(sorti1(u), true, sorti2(h(u)), true), true, ifeq2(sorti2(v(h(u))), true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), j(op2(v(h(u)), h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 1 (ax3) }
% 0.20/0.28 tuple(ifeq2(ifeq(true, true, sorti2(h(u)), true), true, ifeq2(sorti2(v(h(u))), true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), j(op2(v(h(u)), h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.28 tuple(ifeq2(sorti2(h(u)), true, ifeq2(sorti2(v(h(u))), true, op1(j(v(h(u))), j(h(u))), j(v(h(u)))), j(op2(v(h(u)), h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by lemma 10 R->L }
% 0.20/0.28 tuple(ifeq2(sorti2(h(u)), true, ifeq2(sorti2(v(h(u))), true, op1(j(v(h(u))), j(h(u))), j(op2(v(h(u)), h(u)))), j(op2(v(h(u)), h(u)))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 9 (co1_4) }
% 0.20/0.28 tuple(j(op2(v(h(u)), h(u))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by lemma 10 }
% 0.20/0.28 tuple(j(v(h(u))), sorti1(j(v(h(u)))))
% 0.20/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.28 tuple(j(v(h(u))), ifeq(true, true, sorti1(j(v(h(u)))), true))
% 0.20/0.28 = { by axiom 4 (ax4_1) R->L }
% 0.20/0.28 tuple(j(v(h(u))), ifeq(ifeq(sorti2(h(u)), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true))
% 0.20/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.28 tuple(j(v(h(u))), ifeq(ifeq(ifeq(true, true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true))
% 0.20/0.28 = { by axiom 1 (ax3) R->L }
% 0.20/0.28 tuple(j(v(h(u))), ifeq(ifeq(ifeq(sorti1(u), true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true))
% 0.20/0.28 = { by axiom 6 (co1) }
% 0.20/0.28 tuple(j(v(h(u))), ifeq(ifeq(true, true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true))
% 0.20/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.28 tuple(j(v(h(u))), ifeq(sorti2(v(h(u))), true, sorti1(j(v(h(u)))), true))
% 0.20/0.28 = { by axiom 5 (co1_3) }
% 0.20/0.28 tuple(j(v(h(u))), true)
% 0.20/0.28 % SZS output end Proof
% 0.20/0.28
% 0.20/0.28 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------